Continuous Majorization, Wigner Negativity, and QFT

Abstract: 

In d-dimensional discrete variable quantum computing, states with Wigner negativity (also known as magic states) act as a resource for quantum advantage. The loss of magic can be tracked by various monotones, and computation using "easy gates" gives a majorization order between input and output states. In the continuous variable case (Fock space and QFT), Wigner negativity is similarly a resource, but the rest of the story is more intricate. I discuss a proposal to define continuous majorization in quantum phase space, its role in Gaussian operations, and connection to Wigner negativity.Most of my talk will be introduction and review.